(1) Background: Loyalty programmes are business strategies aimed at increasing customer fidelity to brands. One of the most promising technologies of the 21st century is blockchain, whose application to the management of loyalty programmes can increase transparency and reliability, enable interoperability, and facilitate centralised management. (2) Methods: This study evaluates the antecedents of the acceptance of blockchain-based loyalty programmes (BBLPs) using a model grounded in the technology acceptance model UTAUT2. The four basic constructs of UTAUT, which we call the UTAUT-baseline, are considered explanatory factors: performance expectancy (PER), effort expectancy (EFF), social influence (SOC), and facilitating conditions (FAC). Additionally, we consider the constructs introduced in UTAUT2: hedonic motivation (HED) and perceived price value (PRI), to which we add innovativeness (INN) and trust (TRU), and we refer to these as UTAUT-extended, along with the moderating variables of UTAUT and UTAUT2: gender, age, and experience. The analytical approach used is complexity theory, which aims to capture the configurations that lead to both acceptance and rejection positions regarding BBLPs. This analysis is performed via fuzzy set qualitative comparative analysis (fsQCA). (3) Results: Eight explanatory configurations of the acceptance of BBLPs have been obtained, in which the presence of all UTAUT-baseline and UTAUT-extended constructs is a condition in at least three prime implicates. The constructs with the greatest presence as core conditions are PER, EFF, and TRU. On the other hand, nine configurations leading to the rejection of BBLPs have been identified. The absence of all UTAUT-baseline and UTAUT-extended variables is a condition in at least three configurations. The core conditions with the greatest presence in the rejection of BBLPs are the lack of FAC, HED, and PRI. (4) Practical implications: The results obtained are of great interest to business owners, as they allow for the characterisation of different profiles of people potentially engaged with BBLPs, as well as the profiles of consumers reluctant to adopt them.